Hans Rademacher

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Hans Adolph Rademacher (3 April 1892, Wandsbeck, now Hamburg-Wandsbek – 7 February 1969, Haverford, Pennsylvania, USA) was a German mathematician, known for work in mathematical analysis and number theory.

Biography[edit]

Rademacher received his Ph.D. in 1916 from Georg-August-Universität Göttingen; Constantin Carathéodory supervised his dissertation.[1] He was dismissed from his position at the University of Breslau by the Nazis in 1933 due to his public support of the Weimar Republic,[2] and emigrated from Europe in 1934.

After leaving Germany, he moved to Philadelphia and worked at the University of Pennsylvania until his retirement in 1962; he held the Thomas A. Scott Professorship of Mathematics at Pennsylvania from 1956 to 1962. Rademacher had a number of well-known students, including George Andrews, Paul T. Bateman, Theodor Estermann and Emil Grosswald.

Research[edit]

Rademacher performed research in analytic number theory, mathematical genetics, the theory of functions of a real variable, and quantum theory. Most notably, he developed the theory of Dedekind sums. In 1937 Rademacher discovered an exact convergent series for the partition function P(n) , the number of integer partitions of a number, improving upon Ramanujan's asymptotic non-convergent series and validating Ramanujan's supposition that an exact series representation existed.

Awards and honors[edit]

With his retirement from the University of Pennsylvania, a group of mathematicians provided the seed funding for The Hans A. Rademacher Instructorships, and honored him with an honorary degree as Doctor of Science.

Works[edit]

  • with Otto Toeplitz: Von Zahlen und Figuren. 1930. 2nd edn. 1933. Springer 2001, ISBN 3-540-63303-0.
  • with Ernst Steinitz Vorlesungen über die Theorie der Polyeder- unter Einschluss der Elemente der Topologie. Springer 1932, 1976.
  • Generalization of the Reciprocity Formula for Dedekind Sums. In: Duke Math. Journal. Vol. 21, 1954, pp. 391–397.
  • Lectures on analytic number theory. 1955.
  • Lectures on elementary number theory. Blaisdell, New York 1964, Krieger 1977.
  • with Grosswald: Dedekind sums. Carus Mathematical Monographs 1972.
  • Topics in analytic number theory.[3] ed. Grosswald. Springer Verlag, 1973 (Grundlehren der mathematischen Wissenschaften).
  • Collected papers. 2 vols. ed. Grosswald. MIT press, 1974.
  • Higher mathematics from an elementary point of view. Birkhäuser 1983.

Further reading[edit]

  • George E. Andrews, David M. Bressoud, L. Alayne Parson (eds.) The Rademacher legacy to mathematics. American Mathematical Society, 1994.
  • Lexikon bedeutender Mathematiker. Deutsch, Thun, Frankfurt am Main, ISBN 3-8171-1164-9.
  • Tom Apostol: Introduction to Analytical number theory. Springer
  • Tom Apostol: Modular functions and Dirichlet Series in Number Theory. Springer
  • Berndt, Bruce C. (1992). "Hans Rademacher (1892–1969)" (PDF). Acta Arithmetica 61: 209–231. Retrieved 2009-02-07.  Obituary and list of publications.

See also[edit]

References[edit]

  1. ^ Hans Rademacher at the Mathematics Genealogy Project.
  2. ^ Siegmund-Schultze, Reinhard (2009). Mathematicians fleeing from Nazi Germany: individual fates and global impact. Princeton University Press. p. 69. ISBN 978-0-691-14041-4. .
  3. ^ Stark, H. M. (1975). "Review: Hans Rademacher, Topics in analytic number theory". Bull. Amer. Math. Soc. 81 (4): 663–672. doi:10.1090/s0002-9904-1975-13815-8. 

External links[edit]